IJPAM: Volume 52, No. 3 (2009)

AN ANALYSIS OF A COVOLUME METHOD
FOR THE STATIONARY NAVIER-STOKES EQUATIONS

Do Y. Kwak$^1$, D. Bayanjargal$^2$
$^{1,2}$Department of Mathematical Science
Korea Advanced Institute of Science and Technology (KAIST)
335, Gwahangno (373-1, Guseong-Dong), Yuseong-Gu
Daejeon, 305-701, SOUTH KOREA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.We introduce a covolume method for approximating the stationary Navier-Stokes equations and analyze the convergence of the covolume approximation. The covolume method uses the primal and dual partitions. The velocity is approximated using nonconforming piecewise linear functions and the pressure piecewise constants. We use an abstract theory to the study of the convergence of the covolume method for the Navier-Stokes equations, which is based on the results of approximation for branches of nonsingular solutions of nonlinear problems presented in [#!3!#]. Numerical results using a simple Picard type of iteration for solving the discrete Navier-Stokes equations are provided.

Received: March 9, 2009

AMS Subject Classification: 76D05, 35Q30

Key Words and Phrases: covolume method for approximating, stationary Navier-Stokes equations, numerical results

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 3